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小天体动能撞击防御中动量传递因子敏感参数分析

周琪 郑建华 李明涛

周琪, 郑建华, 李明涛. 小天体动能撞击防御中动量传递因子敏感参数分析[J]. 空间科学学报, 2022, 42(3): 463-475. doi: 10.11728/cjss2022.03.210126013
引用本文: 周琪, 郑建华, 李明涛. 小天体动能撞击防御中动量传递因子敏感参数分析[J]. 空间科学学报, 2022, 42(3): 463-475. doi: 10.11728/cjss2022.03.210126013
ZHOU Qi, ZHENG Jianhua, LI Mingtao. Analysis of Sensitive Parameters of Momentum Transfer Factor in Kinetic Impact Defending Small Bodies (in Chinese). Chinese Journal of Space Science, 2022, 42(3): 463-475. DOI: 10.11728/cjss2022.03.210126013
Citation: ZHOU Qi, ZHENG Jianhua, LI Mingtao. Analysis of Sensitive Parameters of Momentum Transfer Factor in Kinetic Impact Defending Small Bodies (in Chinese). Chinese Journal of Space Science, 2022, 42(3): 463-475. DOI: 10.11728/cjss2022.03.210126013

小天体动能撞击防御中动量传递因子敏感参数分析

doi: 10.11728/cjss2022.03.210126013
基金项目: 国防科工局空间碎片和小行星专项资助(kjsp2020020101)
详细信息
    作者简介:

    周琪:E-mail:zhouqi18@mails.ucas.ac.cn

  • 中图分类号: V412

Analysis of Sensitive Parameters of Momentum Transfer Factor in Kinetic Impact Defending Small Bodies

  • 摘要: 动量传递因子 $ \beta $ 是评估动能撞击效果的重要参量。根据动能撞击过程中动量传递因子的理论模型,分析了撞击器特性参数和小天体结构特性参数对动量传递因子取值的影响,并对不同动能撞击方案以及不同材料特性小天体的成坑效应和动量传递因子进行分析。研究表明:标度律参数 $ \mu $$ \beta $ 影响较大, $ \mu $ 是地面实验拟合得到的系数,与材料强度特性相关;当小天体为单体岩石结构时,撞击器速度及密度、小天体密度及表面强度对 $ \beta $ 影响较大,而撞击器半径和小天体引力对 $ \beta $ 影响较小;当小天体为碎石堆结构时, $ \beta $ 对撞击器特性参数和小天体特性参数不敏感,且数值较小。对三种不同动能撞击方案的成坑效应与动量传递因子形成规律进行研究,发现撞击器初始动能对 $ \beta $ 影响较大。当小天体为单体岩石结构时,其对应的动量传递因子取值较大,而当小天体为碎石堆结构时,其对应的 $ \beta $ 取值较小且基本不变。对相同动能撞击方案下不同材料特性小天体(C型、S型和X型小行星)产生的撞击效应进行分析,发现在引力主导时,βC>βS >βX,而在强度主导时 $ \beta $ 取值较小且基本相同。

     

  • 图  1  超过5500颗小行星自转周期与预估直径之间的关系

    Figure  1.  Relationship between rotation periods and estimated diameters of more than 5500 asteroids

    图  2  小天体表面的5种类型

    Figure  2.  Five types of surfaces of small bodies

    图  3  引力主导时动量传递因子随各参数的分布(材质孔隙率30%~40%)

    Figure  3.  Distribution of momentum transfer factor β with each parameter when gravity dominates (Porosity of the material is between 30% and 40%)

    图  4  强度主导时动量传递因子随各参数的分布

    Figure  4.  Distribution of momentum transfer factor β with each parameter when strength dominates

    图  5  引力主导时三种不同动能撞击方案的成坑效应与动量传递因子

    Figure  5.  Cratering effects and momentum transfer factors for kinetic impact schemes of three types when gravity dominates

    图  6  强度主导时三种不同动能撞击方案的成坑效应与动量传递因子

    Figure  6.  Cratering effects and momentum transfer factors for kinetic impact schemes of three types when strength dominates

    图  7  引力主导时末级动能撞击三种不同类型小行星的撞击效应指标

    Figure  7.  Index of impact effects for asteroids of three different types with final kinetic impact when gravity dominates

    图  8  强度主导时末级动能撞击三种不同类型小行星的撞击效应指标

    Figure  8.  Index of impact effects for asteroids of three different types with final kinetic impact when strength dominates

    表  1  可参考的材料经验参数

    Table  1.   Experience parameters of materials

    材料结构编号12345
    主导因素引 力强 度强 度强 度强 度
    材料类型粗 砂石 块弱胶合玄武岩致密沙土珍珠岩/沙土混合物
    宏观孔隙率n/(%)$ 35\pm 5 $0204560
    $ {\mu } $0.410.550.460.40.35
    $ {\nu } $0.40.40.40.40.4
    $ {{C}}_{1} $0.551.50.180.550.6
    $ {k} $0.30.30.30.30.32
    $ {{H}}_{1} $(引力)0.59
    $ {{H}}_{2} $(强度)1.10.380.40.81
    $ {{n}}_{1} $1.21.21.21.21.2
    $ {{n}}_{2,{G}} $(引力)1.3
    $ {{n}}_{2,{S}} $(强度)1111
    撞击器密度$ {\delta } $/($ \text{kg}\cdot {\text{m}}^{-3} $)122027002700930940
    撞击器半径$ {r}(\times {10}^{-3}) $/$ \rm{m} $$ 3.9 $$ 1.6 $$ 3.6 $$ 7 $$ 8.7 $
    撞击速度$ {u} $/($ \text{km}\cdot {\rm{s}}^{-1} $)6-76.21.81.91.8
    目标密度$ {\rho } $/($ \text{kg}\cdot {\text{m}}^{-3} $)15103000260015001200
    引力加速度g/($ \text{m}\cdot {\text{s}}^{-2} $)9.81
    Y/kPa$ 3\times {10}^{4} $$ 4.5\times {10}^{2} $$ 4 $$ 2 $
    下载: 导出CSV

    表  2  特性参数可取值范围

    Table  2.   Range of property parameters

    特性参数取值范围备注
    撞击速度$ u/ $($ \mathrm{k}\mathrm{m}\cdot {\mathrm{s}}^{-1} $) $ 1 \sim 10 $ 撞击器的典型撞击速度[28,29]
    撞击器密度$ \delta / $($ \mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3} $) $ 300 \sim 3000 $ 考虑撞击器类型为两种:人造撞击器或者太空岩石[28,29]
    撞击器半径$ \;\;r $($ \times {10}^{-3})/\mathrm{m} $ $ 1 \sim 10 $ 地面针对动能撞击小天体的撞击实验中撞击器半径设定在$ {10}^{-3} \sim {10}^{-2}\;\mathrm{m} $ 量级[4]
    小天体密度$ \rho / $($ \mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3} $) $ 600 \sim 6000 $ 考虑小天体中彗星密度最小,金属小行星密度最大[30-32]
    小天体引力加速度$ g $($ \times {10}^{-5})/(\mathrm{m}\cdot {\mathrm{s}}^{-2} $) $ 1 \sim 10 $ 考虑小天体典型弱引力场数值在$ {10}^{-5} \sim {10}^{-4}\;\mathrm{m}\cdot {\mathrm{s}}^{-2} $量级[33],小天体尺寸 在6~600 m量级
    小天体表面内聚强度$ Y/ $kPa $ 1\times {10}^{-1} \sim 1\times {10}^{5} $ 考虑小天体中彗星的孔隙率较大,表面内聚强度最小,在$ 100\;\mathrm{P}\mathrm{a} $以上, 而金属小行星密度大,表面内聚强度最大,在$ 100\;\mathrm{M}\mathrm{P}\mathrm{a} $左右[30,32]
    标度律参数$\;\; \mu $ $ 1/3 < \mu < 2/3 $ $ \mu $取值范围为其最大可取范围[4,20]
    下载: 导出CSV

    表  3  引力/强度主导时参数与动量传递因子相关性

    Table  3.   Correlation between parameters and momentum transfer factor when gravity/strength dominates

    参数主导因素与 $ \beta $ 的相关性
    参数$ \mu $ 引力/强度主导 正相关
    撞击器密度$ \delta / $($ \mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3} $) 引力/强度主导 正相关
    撞击器半径$ r $($ \times {10}^{-3})/\mathrm{m} $ 引力主导 负相关
    强度主导 不相关
    撞击速度$ u/ $($ \mathrm{k}\mathrm{m}\cdot {\mathrm{s}}^{-1} $) 引力/强度主导 正相关
    小天体密度$ \rho / $($ \mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3} $) 引力/强度主导 负相关
    小天体引力加速度$ g $ ($ \times {10}^{-5})/(\mathrm{m}\cdot {\mathrm{s}}^{-2} $) 引力/强度主导 负相关
    小天体表面内聚强度$ Y/ $kPa 引力/强度主导 负相关
    下载: 导出CSV

    表  4  Apophis小行星参数

    Table  4.   Parameters of Apophis asteroid

    参数 遥感探测数据
    小行星直径$ R/\mathrm{m} $$ {375}_{-10}^{+14} $
    小行星密度$ \rho / $($ \mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3} $)$ (3.2\pm 0.2)\times {10}^{3} $(LL型球粒陨石)
    小行星宏观孔隙率$ n/ $(%)$ 0 \sim 50 $(平均:20)
    小行星质量$ M $($ \times {10}^{10})/\mathrm{k}\mathrm{g} $$ 4.4 \sim 6.2 $(平均:$ 5.3\pm 0.9 $)
    小行星引力加速度$ g $($ \times {10}^{-5})/(\mathrm{m}\cdot {\mathrm{s}}^{-2} $)$ 8.3511 \sim 11.767 $
    小行星表面逃逸速度$ {v}_{\mathrm{e}\mathrm{s}\mathrm{c}}/ $($ \mathrm{m}\cdot {\mathrm{s}}^{-1} $)$ 0.1770 \sim 0.2101 $
    下载: 导出CSV

    表  5  三种不同动能撞击器参数

    Table  5.   Parameters for kinetic impactors of three types

    参数 经典动能撞击含末级动能撞击以石击石加强型动能撞击
    纯铝材料纯铝材料岩石材料
    有效密度$ \delta / $($ \mathrm{k}\text{g}\cdot {\text{m}}^{-3} $)$ 74.6129 $$ 118.8501 $$ 1457.1070 $
    质量$ m(\times {10}^{3})/\mathrm{k}\mathrm{g} $$ 3.56 $$ 8.75 $$ 200 $
    半径$ r/\mathrm{m} $$ 2.25 $$ 2.6 $$ 3.2 $
    撞击速度$ u/ $($ \mathrm{k}\mathrm{m}\cdot {\mathrm{s}}^{-1} $)$ 6.57 $$ 7.17 $$ 12 $
    撞击动能$ {E}_{{\rm{imp}}}(\times {10}^{10})/\mathrm{J} $$ 7.6834 $$ 22.491 $$ 1440 $
    撞击角$ \varphi / $(°)$ 90 $$ 90 $$ 90 $
    下载: 导出CSV

    表  6  不同类型小行星参数

    Table  6.   Parameters for asteroids of different types

    参数Ryugu小行星Apophis小行星1950 DA小行星
    小行星直径$ R/\mathrm{m} $ $ \left(1.04\times 1.02\times 0.88\right)\times {10}^{3} $ $ {375}_{-10}^{+14} $ $ \left(1.25\pm 0.12\right)\times {10}^{3} $
    小行星密度$ \rho (\times {10}^{3}) $/($ \mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3} $) $ 1.19\pm 0.02 $ $ 3.2\pm 0.2 $ $ 3.5\pm 0.35 $
    小行星宏观孔隙率n/(%) $ > 50 $(高孔隙率) $ 0 \sim 50 $(平均 :20) $ 51\pm 19 $
    小行星质量$ M(\times {10}^{10})/\mathrm{k}\mathrm{g} $ $ 44.975 $ $ 4.4 \sim 6.2 $(平均:$ 5.3\pm 0.9 $) $ 399 $
    小行星引力加速度$ g $($ \times {10}^{-5})/(\mathrm{m}\cdot {\mathrm{s}}^{-2} $) $ 12 $ $ 8.3511 \sim 11.767 $ $ 14.185 \sim 20.850 $
    小行星表面逃逸速度$ {v}_{\mathrm{e}\mathrm{s}\mathrm{c}}/ $($ \mathrm{m}\cdot {\mathrm{s}}^{-1} $) $ 0.3652 $ $ 0.1770 \sim 0.2101 $ $ 0.6234 \sim 0.6865 $
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-01-26
  • 录用日期:  2021-09-26
  • 修回日期:  2022-02-04
  • 网络出版日期:  2022-05-26

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